At one instant a bicyclist is 75 m due east of a park\'s flagpole, going due sou

Question

At one instant a bicyclist is 75 m due east of a park's flagpole, going due south with a speed of 19 m/s. Then, 14 s later, the cyclist is 25 m due north of the flagpole, going due east with a speed of 16 m/s. For the cyclist in this 14 s interval, find the displacement, magnitude and the direction north of west.

I've found the magnitude of sqrt((-75^2)+(25^2)) to be 79.056 m

I'm having problems with the direction which I thought would be arctan(25/-75) which is -18.434 + 180 (because it's in the second quadrant) = 161.565 degrees but that's not the right answer and I can't figure it out. Does the north of west mean more than I think? Hellllppp

Explanation / Answer

North of West means that you start out looking west (180 degrees) like it's 0 degrees, then find the angle between the negative x-axis and your vector.

For example: if you have a vector pointing 135 degrees (that is north of east), then subtract that from 180 to get north of west. So it is the same as saying 45 degrees north of west.
(The easiest way to do this at first might be to turn your paper so the negative x is pointing to the right instead of left - which is a 180 turn hence subtracting from 180)

To get your answer, do 180-161.565.

I hope this helped you!

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